Do nations who have enjoyed the economic benefits of centuries of polluting owe a debt to now-developing countries they're asking to grow greener?

Todd Stern, president Obama's special envoy for climate change, told reporters this week that the U.S. "categorically reject(s)" any "sense of guilt or culpability or reparations". Many voices in the U.S. government, especially those on the obstructive right, get indignant when the subject of climate reparations comes up. Why? Why shouldn't first world countries like the U.S. pay something for the all the pollution we've created since the start of the Industrial Revolution?

Climate reparations are the idea that more developed nations owe a debt to the less developed nations in the form of all the CO2 and greenhouse gases we've dumped into the air over the last couple of hundred years or so. The problem we face — the sheer overload of greenhouse gases in the atmosphere — is one mostly created by America and other first world developed nations. We got away with tens of decades of unregulated and unmitigated pollution and if we expect to ask currently under-developed nations to take a greener (and potentially more expensive upfront) path, we should kick in some money for them to pay for the investments.

Why is the very idea of climate reparations so repugnant to some people? Does fairness have no place in American values? Why shouldn't places like Tuvalu, which even GoDaddy warns is sinking, get some money from the economies that melted the ice caps that raised the seas that swallowed up their land and homes?